We study which functions can be computed by efficient circuits whose gate connections are very easy to compute. We give quasilinear-size circuits for sorting whose connections can be computed by decision trees with depth logarithmic in the length of the gate description. We also show that NL has NC$^2$ circuits ... more >>>

We reduce non-deterministic time $T \ge 2^n$ to a 3SAT
instance $\phi$ of size $|\phi| = T \cdot \log^{O(1)} T$
such that there is an explicit circuit $C$ that on input
an index $i$ of $\log |\phi|$ bits outputs the $i$th
clause, and each output bit of $C$ depends on ... more >>>

We show how to efficiently compile any given circuit $C$
into a leakage-resistant circuit $\widehat{C}$ such that any
function on the wires of $\widehat{C}$ that leaks information
during a computation $\widehat{C}(x)$ yields advantage in
computing the product of $|\widehat{C}|^{\Omega(1)}$ elements
of the alternating group $A_u$. In combination with new
compression ... more >>>

Common presentations of the NP-completeness of SAT suffer
from two drawbacks which hinder the scope of this
flagship result. First, they do not apply to machines
equipped with random-access memory, also known as
direct-access memory, even though this feature is
critical in basic algorithms. Second, they incur a
quadratic blow-up ... more >>>

We study the complexity of black-box constructions of
pseudorandom functions (PRF) from one-way functions (OWF)
that are secure against non-uniform adversaries. We show
that if OWF do not exist, then given as an oracle any
(inefficient) hard-to-invert function, one can compute a
PRF in polynomial time with only $k(n)$ oracle ... more >>>

We put forth several simple candidate pseudorandom functions f_k : {0,1}^n -> {0,1} with security (a.k.a. hardness) 2^n that are inspired by the AES block-cipher by Daemen and Rijmen (2000). The functions are computable more efficiently, and use a shorter key (a.k.a. seed) than previous
constructions. In particular, we ... more >>>